Transform Methods for the Reduction of the Peak to Average

Research ArticleTransform Methods for the Reduction of the Peak toAverage Power Ratio for the OFDM Signal

Rajendra Kumar and Vuttipol Santitewagul

Department of Electrical Engineering California State University Long Beach CA 90840 USA

Correspondence should be addressed to Rajendra Kumar rajendrakumarcsulbedu

Received 26 July 2016 Revised 5 September 2016 Accepted 15 September 2016 Published 12 January 2017

Academic Editor Michael McGuire

Copyright copy 2017 R Kumar and V Santitewagul This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The paper presents multitransform OFDM-OP system for an effective PAPR (peak to average power ratio) reduction that has areasonable computational requirement does not introduce any distortion needs relatively insignificant decrease in the bandwidthefficiency and provides a PAPR very close to that for the single carrier modulation systems thus effectively eliminating any PAPRpenalty incurred by the multicarrier OFDM systemThe PAPR system consists of a bank of multiple orthonormal transforms and aminimumPAPR evaluation unit for finding the optimum transform indexThe paper also presents a hybridOFDM-OP-DSI systemcomprised of the multiple transforms and a novel dummy symbol insertion The PAPR reduction performance of the presentedsystems is compared with those of the various other transform techniques of the literature Various simulations on the presentedsystems show that these can achieve a PAPR that is very close to that of a single carrier system for QAMmodulation with the orderof modulation selected to be 16 64 and 256

1 Introduction

Broadband wireless systems are in a rapidly evolutionaryphase in terms of development of various technologies devel-opment of various applications deployment of various ser-vices and generation ofmany important standards in the field[1ndash28] Orthogonal Frequency Division Multiple Accessing(OFDM) techniques offer efficient bandwidth utilization andprovide many other advantages such as some immunityagainst the distortion due to the multipath propagationenvironment Therefore the OFDM techniques have beenadapted in many wireless communication and sensor stan-dards such as the Worldwide Interoperability for MicrowaveACCESS (WiMAX) digital audio broadcasting (DAB) dig-ital video broadcasting-terrestrial (DVB-T) and Long TermEvolution (LTE)

However the use of a relatively large number of carriersused in the OFDM signal results in a relatively high peakto average power ratio resulting in a much reduced radiofrequency (RF) power amplifier efficiency and distortion dueto the amplifier nonlinearity In order to keep the distortionto some specified limit the output RF power is backed off

from the maximum available power at the amplifier outputIn addition to the reduced output power the output backoffconcurrently also results in the DC to RF power conversionefficiency A detailed analysis of the distortion effects ofthe nonlinear power amplifier and some of the mitigatingtechniques are presented for example in [8 9] and thereferences therein Another problem arising due to distortioncaused by the amplifier is the spreading of the spectrumof theOFDM signal outside the allocated band [10]

Thus there has been strong motivation to come up withtechniques that can reduce the peak to average power ratioof the OFDM signal without causing any distortion in theprocess of transformation or losing in terms of bandwidth orother efficiencymeasuresThe paper presentsmultitransformOFDM-OP system for an effective PAPR (peak to averagepower ratio) reduction that has a reasonable computationalrequirement does not introduce any distortion needs rela-tively insignificant decrease in the bandwidth efficiency andprovides a PAPR very close to that for the single carriermodulation systems thus effectively eliminating any PAPRpenalty incurred by the multicarrier OFDM system

HindawiWireless Communications and Mobile ComputingVolume 2017 Article ID 1421362 17 pageshttpsdoiorg10115520171421362

2 Wireless Communications and Mobile Computing

Serialto

parallelconvertor

(SP)

Parallelto

serialconvertor

(PS)

Inversefast

Fouriertransform

(IFFT)

Inputdata

Basebandmodulator

Guardinterval

insertionblock

Bandlimiting

filterCarrier

modulatord(k) s(k)

X1(k)

X2(k)

XN(k)

x1(k)

x2(k)

xN(k)

OFDMsignal(t)gs(t)gs(n) gse(n)

Figure 1 Block diagram of the OFDM system

The contents of the paper are organized as followsSection 2 of the paper presents a brief introduction to theOFDM system along with various notations used in thepaper Section 3 provides a brief review of the various peakto average power ratio (PAPR) reduction techniques in thepublished literature Section 4 presents multitransform sys-tems and methods recently invented by the first author ofthe paper and taught in US Patent 8995542 March 2015[11] for an effective PAPR reduction which have a reasonablecomputational requirement do not introduce any distortionneed relatively insignificant decrease in the bandwidth effi-ciency and provide PAPR very close to that for the singlecarrier modulation systems thus effectively eliminating anyPAPR penalty incurred by the multicarrier OFDM systemSection 5 presents simulation results on the performance ofthe various PAPR reduction techniques Section 6 presentssome concluding remarks

2 OFDM System

An OFDM-modulated signal consists of the parallel trans-mission of several signals that are modulated at differentcarrier frequencies evenly spaced by Δ119891 [1ndash7] The complexvalued input symbol sequence 119904(119895) is split into 119873 subse-quences 119904119898(119896) with 119904119898(119896) = 119904(119899) 119899 = 119896119873 + 119898 119898 =0 1 119873 minus 1 119896 = 0 1 2 The symbol subsequence119904119898(119896) modulates a corresponding subcarrier at frequency119891119898 for 119898 = 0 1 119873 minus 1 Thus the time sampled versionof the complex envelope 119892119904(119899) of the modulated signal isgiven by (1) wherein the sampling period 119879119878 = 1198790119873 with1198790 denoting the symbol period for the subsequence 119904119898(119895)119892119904 (119899 + 119896119873) = 1radic119873

119873minus1sum119898=0

119904119898 (119896) exp [1198952120587119898119899119873 ] 119899 = 0 1 119873 minus 1 119896 = 0 1

(1)

The consecutive 119873 samples of 119892119904(119899) constitute an OFDMsymbol and according to (1) the samples during the 119896thOFDM symbol may be obtained by an119873 point IFFT (inversefast Fourier transform) of the consecutive 119873 symbols in thesymbol sequence 119904(119895) or the 119896th symbols in the symbolsubsequences 119904119898(119896) 119898 = 0 1 (119873 minus 1) In the multipleaccess application of OFDM the symbol subsequence 119904119898(119896)may be the symbol sequences generated for the 119873 multipleaccess users rather than subsequences of a single user symbol

sequence The OFDM signal has a guard interval of length119879119866 for each OFDM symbol to mitigate the intersymbolinterference The sample values during any guard intervalare obtained by the periodic extension of the subsequent 119873sample values of 119892119904(119899) The transmitted radio frequency (RF)OFDM signal V(119905) is given by

V (119905) = Re 119892119904 (119905) exp [1198952120587119891119888119905] (2)

where 119891119888 denotes the carrier frequency and 119892119904(119905) denotesthe continuous time signal obtained by interpolation of thesampled signal 119892119904(119899) using for example 0th order hold Thesignal 119892119904(119899)may also be band limited by a band limiting filtersuch as the square root raised cosine filter in generating theanalog signal 119892119904(119905)

Figure 1 shows the block diagram of the OFDM sys-tem Referring to Figure 1 the data 119889(119896) that may be abinary stream is inputted to the baseband modulator blockthat modulates the input data according to a modulationscheme that is selected to be the QAM modulation Theresults of the paper will apply equally well to various othermodulation techniques such as MPSK or MASK modulationschemes The complex baseband signal 119904(119896) 119896 = 0 1 isinputted to the serial to parallel converter with the outputgiven by the OFDM modulation symbol vector 119883(119896) =[1198831(119896) 1198832(119896) sdot sdot sdot 119883119873(119896)]119879 where 119883119898(119896) = 119904119898(119896) or119883119898(119896) = 119904(119899) 119899 = 119896119873 + 119898 119898 = 0 1 119873 minus 1119896 = 0 1 The inverse fast Fourier transform (IFFT) blockprovides the inverse Fourier transform of 119883(119896) providingthe OFDM modulated signal vector 119909(119896) of dimension 119873also referred to as the OFDM frame at the output that isinputted to the parallel to serial converter block The parallelto serial converter block concatenates the components 119909119898(119896)of the vector119909(119896)providing the basebandOFDMsignal119892119904(119899)119899 = 119896119873 + 119898 given by (1) The complex baseband OFDMsignal 119892119904(119899) is inputted into the guard band insert block forextending the OFDM signal duration by the guard interval119879119866 by a periodic extension of the signal 119892119904(119899) The OFDMbaseband signal with a guard interval denoted by 119892119904119890(119899) isinputted to a band limiting filter that may be for examplea square root raised cosine filter and may include a digitalto analog converter providing the filtered complex basebandOFDM signal 119892119904(119905) that modulates a carrier signal providingthe bandpass OFDM signal V(119905) given by (2) This paperis focused upon the subsystem of the OFDM system that

Wireless Communications and Mobile Computing 3

generates the complex basebandOFDM signal 119892119904(119899) from theinput data 119889(119896)

The peak to average power ratio PAPR is defined as

PAPR = 10 logmax119905

1003816100381610038161003816119892119904 (119905)10038161003816100381610038162119864 [1003816100381610038161003816119892119904 (119905)10038161003816100381610038162] (3)

In (3) 119864 denotes the expected value As 119892119904(119905) is a randomprocess PAPR is a random variable with some probabilitydistribution function or equivalently in terms of a cumulativedistribution function (CDF) or equivalently the complemen-tary cumulative distribution function (CCDF) 119866(120574) that isfunction of the real variable 120574 given by 119866(120574) equiv ProbPAPR gt120574 It is of interest tominimize the119866(120574) for any specified valueof 120574 by some possible invertible transform of the signal 119892119904(119905)In practice the PAPR is defined in terms of the modulatedsignal vector 119909(119896) as

PAPR cong max1198991003816100381610038161003816119909119899 (119896)10038161003816100381610038162119909 (119896)2 119873 (4)

and the CCDF is defined in terms of the time samples of thePAPR in (4)

3 Techniques for the Reduction ofthe Peak to Average Power Ratio

There have been several solutions proposed in the literatureto reduce the peak to average power ratio of the OFDMsignal One such method is the clipping method [12] whereinthe signal above a certain specified value is clipped This issimilar to the clipping by the amplifier and thus introducesdistortion however clipping and filtering the signal beforeinputting to the RF amplifier may mitigate the problemof spectrum spreading that is encountered by the clippingcaused by the amplifier

In another PAPR reduction method proposed in [13]and termed the selective mapping (SLM) method consistsof forming 119876 vectors 119875119902 119902 = 1 2 119876 with 119876 an integerbeing formed with the 119894th element of the vector 119875119902 selectedequal to 119875119902119894 = exp[119895120593119902119894 ] 119895 = radicminus1 119894 = 0 1 119873 minus 1 Thephase 120593119902119894 is selected in a random manner with a uniformprobability density function over the interval [0 2120587] Theset of vectors thus formed is made known to the receiverin advance For any time 119896 the OFDM modulation symbolvector 119883(119896) is component-wise multiplied by each of the119876 vectors 119875119902 resulting in the modified vector 119883119902(119896) 119902 =1 2 119876 This follows evaluation the inverse fast Fouriertransform (IFFT) 119909119902(119896) of 119883119902(119896) and computing the peak toaverage power ratio of the OFDM modulation signal vector119909119902(119896) for 119902 = 1 2 119876 The vector 119909119902(119896)with the minimumPAPR is selected for transmission with the correspondingindex 1199020 made available to the receiver as a side informationThe result presented in [13] for the case of 119873 = 128 and119876 = 4 andQPSKmodulation shows an improvement of about3 dB at a PAPR value corresponding to the complementaryprobability distribution function (CPDF) value of 10minus3

In the partial transmit sequence (PTS) method proposedin [14] the set of indices 0 through119873 minus 1 is partitioned into119881 disjoint subsets 119878V V = 1 2 119881 wherein each of the119881 subsets has (119873119881) indices For V equal to 1 through 119881a vector 119883V(119896) of length 119873 is obtained with all its elementsequal to 0 except the ones with indices in the subset 119878V thatare selected to be equal to the corresponding elements ofthe vector 119883(119896) resulting in 119883(119896) = sum119881V=1119883V(119896) Each ofthe 119881 vectors is inverse Fourier transformed using the IFFTproviding the 119881 signal vectors 119909V(119896) = Fminus1119883V(119870) whereinFminus1 denotes the inverse Fourier transformThe signal vectorsare multiplied by the complex scalars exp[119895120593V(119896)] with 120593Vselected randomly and are uniformly distributed over theinterval (0 2120587) The weighted signal vectors are summed andthe PAPR of the resulting sum is computed The PAPR isminimized over the selection of the scalars exp[119895120593V(119896)] andthe result of such a minimization is selected for transmissionThe selected coefficients are provided to the receiver as a sideinformation The simulation results in [14] show that for thecase of 119881 = 119876 and for QPSK modulation the PTS schemeprovides a better performance compared to that of the SLMmethod

A dummy sequence insertion (DSI) method of the PAPRreduction has been proposed in [16] In the DSI methodthe vector 119883(119896) is comprised of119873119868 modulation symbols and119873119863 = (119873 minus 119873119868) dummy symbols resulting in 119883(119896) =[119883119868119879(119896) 119883119863119879(119896)]119879 wherein 119879 denotes the matrix transposeand 119883119868(119896) and 119883119863(119896) are the vectors of length of 119873119868 and119873119863 and comprised of the modulation symbols and dummysymbols respectively The DSI method results in a reductionof the bandwidth efficiency by a factor of (119873119868119873) howeverit does not require any side information The selection ofthe dummy sequence is comprised of an initial step anda recursive step that modifies the dummy sequence untilthe PAPR of 119909(119896) = Fminus1119883(119870) is below a threshold orthe number of recursions exceeds some maximum permis-sible number of recursions Four different methods for theselection of the dummy sequence are suggested in [16] Inthe first method the dummy sequence is comprised of acomplementary sequence [16] with different complementarysequences selected in the recursive step In another methodthe initial dummy sequence is selected to be an all 0 or an all1 sequence with the recursion step comprised of sequentiallyflipping the dummy sequence bits until the PAPR belowthe threshold value is achieved or the number of recursionsexceeds a specified limit

In the method of selective scrambling proposed in [17]the message bit sequence is scrambled by each of the fourmaximal lengths or m-sequences that are not cyclicallyshifted versions of each other with the two bits repre-senting the index 119902 of the m-sequence appended to thescrambled sequenceThe scrambled sequences aremodulatedinto QPSK symbols resulting in the OFDM modulationsymbol vectors119883119902(119896) which are inverse Fourier transformedresulting in the OFDM modulated signal vectors 119909119902(119896) for119902 = 1 2 3 and 4 The vector among the 4 vectors 119909119902(119896) witha minimum PAPR is selected for transmission This methodis very similar to the SMI method with the difference that


it is the bit sequence that is scrambled instead of the QPSKmodulation symbol sequence in the SMI method

In the block coding schemes for the PAPR reduction theOFDMmodulation symbol vector119883(119896) is transformed usingone of the block error correction codes [18ndash20] For examplethe use of complementary sequence codes is presented in[18] While the use of the block error correction codes toreduce the PAPR while simultaneously achieving the errorcorrection capability of the code is clearly very appealinghowever the presently studied methods based on blockerror correction codes may require relatively very low ratecodes resulting in relatively poor bandwidth efficiency atrelatively high number of carriers To quote from [18] theauthors state that ldquoThe major drawback of the peak powercontrolling block coding scheme is that the coding rate isinversely proportional to the number of OFDM subcarriersFor example for permissible PAPR of 6 dB the coding rate ofthe 128-subcarrier system becomes 764 = 011 which clearlyseems quite impractical for many applicationsrdquo Similarresults appear in [19 20]

In the precoding techniques proposed in [21ndash23] theOFDM modulation symbol vector 119883(119896) is premultiplied byan orthogonal matrix 119875 resulting in the transformed symbolvector 119883119901(119896) = 119875119883(119896) The inverse Fourier transform of thetransformed symbol vector provides the modulated signalvector 119909(119896) for the transmission The precoding matrix 119875 issignal independent and is known to the receiver The orthog-onal transform is selected to be the discreteHartley transform(DHT) in [21] discrete cosine transform in [22] and theWalsh-Hadamard transform (WHT) in [23] respectivelyTheprecoding techniques are very attractive as these do notintroduce any distortion unlike the clipping based methodsdo not result in any reduction in the bandwidth efficiencyas is the case with block coding methods and are relativelysimple in implementation In [23] the precoding techniqueis combined with the SLM and DSI methods for providingfurther improvement in their PAPR reduction capability atthe expense of some additional complexity of implementationand some reduction the bandwidth efficiency It is shown inthis paper that there is a scope for further improving theirPAPR reduction capability while maintaining their desirablecharacteristics

4 Multitransform Method forPAPR Reduction

This section in its entirety describes the multitransformsystems andmethods for the reduction of the peak to averagepower ratio recently invented by the first author of thispaper and taught in and protected by US Patent 8995542March 31 2015 [11] Figure 2 shows the block diagram of theproposedmultitransformmethod As shown in the figure themodulation symbol vector 119883(119896) is transformed by a number119873119879 of transforms providing 119873119879 transformed symbol vectors1198831(119896) 1198832(119896) 119883119873119879(119896) with119883119899 (119896) = 119875119899119883 (119896) 119899 = 1 2 119873119879 119896 = 0 1 2 (5)

The IFFT blocks in Figure 2 provide the IFFT of thetransformed symbol vectors 119883119899(119896) denoted by 119909119899(119896) for 119899 =1 2 119873119879 The input selector block in Figure 2 selectsthe one out of the 119873119879 input vectors 119909119899(119896) with the lowestPAPR computed according to (4) The output of the inputselector block is inputted to the parallel to serial converterthat generates the serial sample sequence 119892119904(119899) at the output

In (5) 119875119899 for 119899 = 1 2 119873 are some convenientlyselected119873times119873 nonsingularmatrices For example with119873119879 =4 the 4 matrices that are selected are the identity matrix119868119873 corresponding to no transform the Walsh-Hadamardtransform (WHT) matrix 119875119882 the discrete cosine transform(DCT) matrix 119875119862 and the discrete Hartley transform (DHT)matrix 119875119867 The three transform matrices are given in termsof their (119898 119899)th element119898 119899 = 1 2 119873 by

119875119867119898119899 = 1radic119873 cos [2120587 (119898 minus 1) (119899 minus 1)119873 ]+ sin [2120587 (119898 minus 1) (119899 minus 1)119873 ]

(6)

119875119862119898119899 = radic 2119873 cos [120587 (119898 minus 05) (119899 minus 05)119873 ] (7)

with the Walsh-Hadamard transform matrix 119875119882 with itselements equal to +1 or minus1 defined recursively in terms of thematrix119882 as

1198822119898 = [1198822119898minus1 1198822119898minus11198822119898minus1 minus1198822119898minus1]

1198822 = [1 11 minus1]

119898 = 2 3

(8a)

119875119882 = 1radic11987311988221198980 119873 = 21198980 (8b)

In the same manner the inverse Fourier transform may beexpressed in terms of the transform matrix 119875119865 given by

119875119865119898119899 = 1radic119873 exp [2120587119895 (119898 minus 1) (119899 minus 1)119873 ] 119895 = radicminus1 (9)

The use of scalar 1radic119873 in (6)ndash(9) introduced for the sake ofclarity makes these matrices orthonormal with 119875119875119867 = 119868119873 or119875minus1 = 119875119867 for any of the transformmatrices 119875 in (6)ndash(9) withthe superscript 119867 denoting the matrix Hermitian transposeand 119868119873 denoting the 119873 times 119873 identity matrix However thescale factor 1radic119873 in (6)ndash(9) may be eliminated withoutintroducing any changes in the performance results forthe OFDM system Due to symmetry the matrices 119875119867119875119882 and 119875119862 are also unitary with 119875minus1 = 119875 The use ofthese orthogonal matrices permits the use of fast transformtechniques permitting the matrix vector multiplication inorder 119873log2(119873) operation instead of requiring order 1198732operations for obtaining the transformed symbol vector


SPconverter

IFFT

IFFT

IFFTInput

selector

OFDMsignal

PSconverter

Inputdata

Basebandmodulator

d(k) s(k) X(k)

X1(k)

X2(k)

x1(k)

x2(k)

x(k)

P1

P2gs(n)

PN119879

XN119879(k) xN119879(k)

Figure 2 Multitransform OFDM system for PAPR reduction

119883119899(119896) In fact the number of operations can be further re-duced by exploiting the relationships between various trans-forms In particular they may be related to the Fourier trans-form For example for a real valued sequence119883119877(119896) its DHTtransform may be obtained by [26 27]

DHT 119883119877 (119896) = Re (1 minus 119895)Fminus1 [119883119877 (119896)] 119895 = radicminus1 (10)

In (10)Fminus1 denotes the inverse Fourier transform and Re(119911)for any complex quantity 119911 denotes the real part of 119911 With119883(119896) = 119883119877(119896) + 119895119883119868(119896) its DHT transformmay be evaluatedas

DHT 119883 (119896) = Re (1 minus 119895)Fminus1 [119883119877 (119896)]+ 119895Re (1 minus 119895)Fminus1 [119883119868 (119896)] (11)

Thus computing the IFFT of 119883119877(119896) and 119883119868(119896) separatelypermits a direct computation of the DHT form (11) requiringonly order119873 operations Of course the IFFT of119883(119896) is givenby

Fminus1 119883 (119896) = F

minus1 [119883119877 (119896)] + 119895Fminus1 [119883119868 (119896)] (12)

The computation of IFFT of 119883(119896) from (12) does not requireany more computations compared to directly computing theIFFT of119883(119896) In the samemanner theWHT of119883119877(119896)may becomputed in terms of the FFT or IFFT of119883119877(119896) For example[29] describes a method of computing the Fourier transformof a real sequence in terms of itsWalsh-Hadamard transformThe relationship given in [29] can be more easily used for thecomputation of WHT from the IFFT For example equation(6) of [29] relates the WHT to the IFFT for the case of119873 = 8requiring only 10 real multiplications equivalent to less than3 complex multiplications Similar computations are given in[29] for more general value of 119873 details are not presentedhere Thus for the case of 119873119879 = 4 the order of transformsand IFFT may be performed as shown in Figure 3

Another example of the multitransform method consistsof the use of 119873119879 gt 4 transform matrices including the 119868

IFFT

DCT IFFT

IFFT

IFFT

X(k) = X1(k)

X1(k)

x1(k)x1(k)

x2(k)

x3(k)

x4(k)

X2(k)

X3(k)

X4(k)

IFFT rarrDHT

IFFT rarrWHT

Figure 3 Order of transform computations (119873119879 = 4)

119875119867 119875119882 and 119875119862 and the possible products of these matricessuch as 119875119867119875119862 Table 2 lists some of these transform matriceswith their associated indices that are referred to in thesimulation results of the next section In the computation ofthe transformed vectors 119909119899(119896) Figure 3 may be used for theminimization of the computational requirements as for thecase of119873119879 = 4 For any pair orthonormal matrices 1198751 and 1198752one obtains

(11987511198752)minus1 = (1198752)minus1 (1198751)minus1 = 11987521198671198751119867 = (11987511198752)119867 (13)

Thus the product of any two orthonormal matrices is alsoorthonormal and all of the 119873119879 transforms selected for thePAPR reduction are orthonormal transforms The set of allpossible (119873times119873) orthonormal matrices forms a group undermatrix multiplication

41 Multitransform Method with Dummy Sequence InsertionThe multiple transform method may be combined with thedummy insertion method resulting in the OFDM-OP-DSImethod for the PAPR reduction wherein OP refers to theoptimum transform In this method the OFDM symbolvector 119883(119896) is comprised of 119873119863 dummy symbols and 119873119868 =119873 minus 119873119863 information symbols The dummy symbols maycorrespond to 119873119863 randomly selected but fixed indices ofthe vector 119883(119896) for example the first 119873119863 elements may bethe dummy symbols Figure 4 shows the block diagram ofthe direct implementation of the OFDM-OP-DSI method InFigure 4 119883119868(119896) is the vector of length 119873 with 119873119868 elementsequal to the information symbols and119873119863 = 119873minus119873119868 elements


+

Dummysymbolsvector

generator

+Input

selector

IFFT

IFFT

IFFT

MinimumPAPR

evaluatorYes

No

PSconverter

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

X1(k)

X2(k)

x1(k)

x2(k)

P1

P2

PAPRmltVT

xo(k)

SPconverter

insertionwith 0 s

sumgs(n)

XI(k)

XD(k) PN119879

XN119879(k) xN119879(k)

Figure 4 Multitransform-DSI OFDM system for PAPR reduction

equal to 0 with the set S119868 comprised of their indices Theelements of the length119873 vector119883119863(119896)with indices the setS119868are equal to the dummy symbols with the other119873119868 = 119873minus119873119863elements set equal to 0 As shown in the figure the vector119883(119896) = 119883119868(119896)+119883119863(119896) is inputted to the119873119879 transform blocksthat multiply the vector 119883(119896) by the matrices 119875119899 providingthe transformed vectors 119883119899(119896) 119899 = 1 2 119873119879 at theiroutputs

The transformed vectors are inputted to the IFFT blocksproviding the inverse Fourier transforms 119909119899(119896) of the trans-formed vectors 119883119899(119896) to the input selector block that selectsthe input with the lowest PAPR from the 119873119879 inputs Asshown in the figure the transformed OFDM signal vectors119909119899(119896) are inputted to the minimum PAPR evaluator blockthat evaluates the minimum of the PAPRs of the 119873119879 OFDMsignal vectors 119909119899(119896) and provides the result PAPRm to thedecision blockThe decision block compares the PAPRm witha threshold 119881119879 If the threshold condition is satisfied theinput selector block selects the input with the minimumPAPR and inputs the selected vector 119909(119896) to the vector toserial converter that outputs the OFDM complex basebandsignal If the threshold condition is not satisfied the processis repeated with a different selection of the dummy symbolsThe selection of the dummy symbols eithermay be performedin a predetermined sequence or may be based on a randomselection strategy Figure 12 shows a histogram of the opti-mum dummy symbol selection for an example of 64 QAMmodulation In the multitransform-DSI method based on athreshold the sequencing of the dummy symbol selectionmay be performed according to the histogram as shown inFigure 12

The computational requirements of the optimum trans-form-DSI method can be significantly reduced by an appro-priate organization of the computations The transformedsignal vector 119909119899(119896)may be expressed as

119909119899 (119896) = 119875119865119875119899119883(119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119883119863 (119896) (14a)

With 1198951 1198952 119895119873119863 denoting the indices of the vector 119883(119896)corresponding to the dummy symbols the vector 119909119899(119896) maybe expressed as

119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119878119910119863 (119896)= 119875119865119875119899119883119868 (119896) + 119875119899119863119910119863 (119896) (14b)

In (14b) 119910119863 is the vector of length119873119863 with its elements equalto the dummy symbols and119875119899119878 is the (119873times119873119863) submatrix of119875119899comprised of the 119873119863 columns of the matrix 119875119899 with indices1198951 1198952 119895119873119863 that is the matrix 119875119899119878 is given by

119875119899119878 = [1198751198991198951 1198751198991198952 sdot sdot sdot 119875119899119895119873119879 ] (15)

and 119875119899119863 denotes the matrix with its columns equal to theinverse Fourier transforms of 119875119899119895119894 119894 = 1 2 119873119863 In (15) 119875119899119895denotes the 119895th column of the matrix 119875119899 for any integer 119895In the specific case of 119873119863 = 1 considered in the simulationspresented in the paper the signal vector 119909119899(119896) may beexpressed as

119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119901119899119904119863 (119896) (16)

In (16) 119904119863(119896) denotes the dummy symbol and 119901119899 is a columnvector given by the Fourier transform of the 119895th column of 119875119899wherein 119895 is the index of the dummy symbol in the OFDMsymbol vector 119883(119896) that may be precomputed and storedfor use in the real time application Thus the change of thedummy symbol requires just the multiplication of a fixedvector 119901119899 by the selected symbol for the selected transformmatrix 119875119899 rather than requiring an 119873 point IFFT for eachsymbol selection and each 119899 resulting in considerable savingin the computational requirements

Figure 5 shows the block diagram of the computationallyefficient OFDM-OP-DSI method for the case of 119873119863 = 1 InFigure 5 119883119868(119896) vector of length 119873 with 119873119868 elements equalto the information symbols and 119873119863 = 119873 minus 119873119868 elements


+

+

Dummysymbols

subvectorgenerator

IFFT

IFFT

IFFT

Yes

No

PSconverter

+

+

++

+

++

Inputselector

MinimumPAPR

evaluator

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

P1

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PAPRm

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SPconverter

insertionwith 0 s

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qNT

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ltVT

sum

sum

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gs(n)

XI(k)

PN119879

xN119879(k)

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yD(k)

XI1(k)

XI2(k)

XIN119879(k)

xI1(k)

xI2(k)

xIN119879(k)

Figure 5 Computationally efficient multitransform-DSI OFDM system for PAPR reduction

equal to 0 with their indices in the set S119868 is inputted tothe 119873119879 transform blocks providing the transformed outputs119883119868119899(119896) for 119899 = 1 2 119873119879 The transformed outputs119883119868119899(119896)are inputted to the IFFT blocks providing the transformedOFDM information signal vectors 119909119868119899(119896) at the outputsAs shown in the figure the dummy symbol vector 119910119863(119896)at the output of the dummy symbol selector is multipliedby the vectors 1198751119863 1198752119863 119875119873119879119863 with the result added to therespective transformed OFDM information signal vectors119909119868119899(119896) resulting in the transformed OFDM signal vectors119909119899(119896) 119899 = 1 2 119873119879

As shown in Figure 5 the transformed OFDM signalvectors 119909119899(119896) are inputted to the minimum PAPR evaluatorblock that evaluates the minimum of the PAPRs of the 119873119879OFDM signal vectors 119909119899(119896) and provides the result PAPRm tothe decision block The decision block compares the PAPRmwith a threshold 119881119879 If the threshold condition is satisfiedthe input selector block selects the input with the minimumPAPR and inputs the selected vector 119909(119896) to the vector toserial converter that outputs the OFDM complex basebandsignal If the threshold condition is not satisfied the processis repeated with a different selection of the dummy symbols

The information about the selected transform can beimbedded into the OFDM signal by using one or moresymbols of the OFDM frame for this purpose For the casewherein the order of modulation119872 is greater than or equalto 64 and the number of transforms 119873119879 is less than 16 asproposed in the paper one symbol is adequate for carryingthis information In fact for 119872 ge 64 significant errorcorrection coding on the transform index may be used toprotect against error Using one symbol for carrying this side

information the number of zeros in the vector119883119868(119896) is madeequal to (119873119863 + 1) Assuming that the side information iscontained in the first element of the OFDM modulationsymbol vector 119883(119896) the vector to be added to the modifiedinformation signal vector 119909119868119899(119896) in Figure 5 is given by

119902119899 = 1198751198651198751198991 119904119899119894 (17)

In (17)1198751198991 denotes the first columnof the transformmatrix119875119899and 119904119899119894 is the symbol containing the index 119899 of the transform ina possibly coded form As shown in Figure 5 the fixed vector(not a function of time 119896) 119902119899 is added as a bias to themodifiedinformation signal vector 119909119868119899(119896) resulting in the modifiedmodulation signal vector 119909119899(119896) given by (18) for the case of119873119863 = 1

119909119899 (119896) = 119909119868119899 (119896) + 119901119899 (119896) + 119902119899 (18)

where in (18) the first term on the right hand side isdependent upon the information symbols 119904119896 at the output ofthe baseband modulator the second term 119901119899(119896) is dependentupon the dummy symbols selected and the last term 119902119899 thatis independent of 119896 provides the side information about theindex of the transform

The selection of the indexing symbol 119904119899119894 used to encodethe transform index 119899 for 119899 = 1 2 119873119879 is made fromthe signal constellation diagram of the complex basebandsignal 119904(119896) so as to minimize the probability of error in thedetection of 119899 at theOFDMreceiver For example for the caseof 64 QAMmodulation with the signal constellation diagramshown in Figure 8 and119873119879 = 16 the indexing symbols may be


ReceivedOFDM signal

RF to complexbasebandconverter

Guardintervaldeletion

block

SPconverter

FFTblock

Transform indexdetection block

Dummyand

indexingdeletion

block

PSconverter

Basebanddemod

xo(k)

d(k)

r(t)

no

Xo(k)

Inversetransform

block(Pn119900 )

gs(n)gse(n)

Figure 6 Multitransform-DSI OFDM system receiver block diagram

selected as shown by the shaded circles in Figure 8 resultingin a minimum distance among the indexing symbols equalto 2119889 compared to the minimum Euclidean distance equalto 119889 among the symbols in the complete signal constellationdiagram thereby minimizing the probability of detectionerror in the transform index 119899 in the OFDM receiver In somecasesmore than one indexing symbolmay be used for furtherreduction of the probability of detection error For exampleusing two symbols for indexing the transform index 119899 maybe encoded by a code word comprised of a pair of symbolsselected from the set of symbols with indices 0 7 56 63 inFigure 8 resulting in a minimum Euclidean distance amongthe code words equal to 7119889radic2 cong 10119889making the probabilityof detection error extremely small

42 Demodulation of theMultitransform-DSI Signal Figure 6shows the block diagram of the receiver for the multi-transform-DSI signal The OFDM RF signal V(119905) receivedin the presence of noise 120585(119905) is down-converted to complexbaseband and possibly filtered by a band limiting filtersuch as the square root raised cosine filter providing thecomplex baseband signal 119892119904119890(119899) to the guard interval deletionunit that removes the guard interval from the complexbaseband signalThe resulting complex baseband signal119892119904(119899)is inputted to the serial to parallel converter that providesthe modified signal vector at the output and given by (18)for some specific value of 119899 = 1198990 selected at the transmitterThe modified signal vector 119909119900(119896) = 1199091198990(119896) is inputted to theFFT block providing the modifiedmodulation symbol vector1198831198990(119896) at the output

Themodifiedmodulation symbol vector1198831198990(119896) is inputtedto the transform index detection unit for detecting thetransform index 1198990 used in the transmitter from the vector1198831198990(119896) In the transform index detection unit the vector1198831198990(119896)

is premultiplied by the vectors 120595119899119867 = [1 0 0 sdot sdot sdot] (119875119899)minus1 =1198751198991198671 with 1198751198991198671 denoting the conjugate transpose of the firstcolumn of the matrix 119875119899 With the vector 120595119899119867 the metrics119903119899(119896) 119899 = 1 2 119873119879 are evaluated as in

119903119899 (119896) = 100381610038161003816100381610038161205951198991198671198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 = 100381610038161003816100381610038161198751198991198671 1198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 119899 = 1 2 119873119879

(19)

In (19) 119904119899119894 is the indexing symbol for the 119899th transformationmatrix 119875119899 From (17) to (19) it follows that ignoring thereceiver noise and the self-noise 119894119904 the index 1199031198990 correspond-ing to the transform 1198751198990 selected at the transmitter is 0 with

119903119899 (119896) = 100381610038161003816100381610038161198751198991198671 11987511989901 1199041198990119894 + 119894119904 minus 119904119899119894 100381610038161003816100381610038162 119899 = 1198990 1199031198990 = 0 (20)

In (20) 119894119904 denotes the self-noise due to the information anddummy symbols Minimizing the metric 119903119899 over 119899 results incorrect detection of 1198990 with some small probability of errordepending upon the transforms 119875119899 for 119899 = 1 through119873119879 andthe indexing symbols 119904119899119894 As shown in Figure 6 the transformindex detection block detects the index of the transform usedin the OFDM transmitter and provides the index 1198990 to theinverse transform block that multiplies the OFDM modifiedsymbol vector 1198831198990(119896) by (1198751198990)minus1 = 1198751198990119867 Dropping thecomponents of 1198831198990(119896) corresponding to the dummy symbolsand the indexing symbol results in a subvector of length119873119868 =(119873 minus 119873119863 minus 1) of the information symbol vector 119883119868(119896) Theresulting vector is inputted to the parallel to serial converterfor providing the sequence of baseband symbols 119904(119896) at theoutput


The self-noise term 119894119904 in (20) may be eliminated by modi-fying the multitransform-DSI implementation in that the119873 times 119873 transform matrices 119875119899 are replaced by the followingpartitioned matrices

119875119899 = [[1 00119879 119875119899]]

(21)

In (21) 0 denotes a row vector of zeros of length (119873minus1) and119875119899is the (119873minus1)times(119873minus1) transformmatrix obtained by deletingthe first row and forts column of 119875119899 The vector 119902119899 in Figure 5is replaced by the vector 119902119899 = 1198751198651 119904119899119894 where 1198751198651 denotes thefirst column of the IFFT transform matrix 119875119865 Equivalentlythe indexing symbol 119904119899119894 is added to the first component of themodified information symbol vector119883119868119899(119896) In the modifiedapproach the indexing symbol is not a part of the transformoperation In the demodulation of themultitransformOFDMsignal Figure 6 ismodified accordinglyThus in the transformindex detection unit the first element11988311989901 of the vector1198831198990(119896)that is equal to the indexing symbol 1199041198990119894 plus receiver noise120585(119896) is used to detect the transform index by theminimization

min119899

100381610038161003816100381611988311989901 minus 119904119899119894 10038161003816100381610038162 = min119899

10038161003816100381610038161199041198990119894 + 120585 (119896) minus 119904119899119894 10038161003816100381610038162 (22)

Except for the change in the operation of the transformindex detection unit the block diagram of the modifiedmultitransform OFDM system is same as that in Figure 6Partition similar to that in (21) may be used for transmissionof any pilot symbols

The following section presents the simulation resultson the performance of the multitransform PAPR reductionOFDM system and compares it with some of the existingmethods for the reduction of the PAPR

5 Simulation Results

This section presents simulation results on the performanceof the multitransform techniques for the PAPR (peak to aver-age power ratio) reduction with a performance comparisonwith the existing precoding and dummy sequence insertion(DSI) based techniques that may be the ones most promisingin terms of the various criteria including minimal reductionin bandwidth efficiency and distortion less transformationThe results for the existingmethods are similar to those in thevarious references of this paper The complementary cumu-lative probability distribution function (CCDF) of the PAPRis obtained by simulation runs of 104 OFDM symbols for allpossible FFT length 119873 Thus the number of QAM symbolssimulated in each run is equal to 119873 times 104 The simulationsare performed with119872QAMmodulation with the number ofpoints119872 in the signal constellation selected equal to 16 64and 256 In case of the dummy sequence insertion schemethe number of dummy symbols is limited to 1 in all of thesimulation results as an increase in the length of the dummysequence provided only marginal improvement at the cost

Im

Re

0 4 8 12

13951

2 6 10 14

1573 11

Figure 7 Signal constellation diagram for 16 QAM signal

0

1

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8 16 24 32 40 48 56

10 18 26 34 42 50 58

9 25 41 5717 33 49

11 27 43 5919 35 51

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of significant increase in computational complexity In theconstellation diagrams the symbols are indexed using theGrey coding scheme Figures 7 and 8 show the constellationdiagram for the case of119872 equal to 16 and 64 respectively

Figure 9 plots the result for the case of the 119873 = 64subcarriers and 16 QAM modulation with and without thedummy symbol insertion wherein the dummy symbol isselected to be any of the 16 possible points in the constellationdiagram Different possible values of the dummy symbolare selected until an improvement in the PAPR exceeds thespecified threshold value of 04 dB As may be inferred fromFigure 9 an improvement of about 04 dB is achieved withthe insertion of the dummy symbol Figure 10 shows thecorresponding result when all 16 possible symbol values aretried in an exhaustivemanner and the one providing themostimprovement in the PAPR is selected As may be inferred


2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)

Figure 9 CCDF of OFDM-DSI system for 16 QAM (04 dB thresh-old)

2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)

Figure 10 CCDF of OFDM-DSI system for 16 QAM (exhaustivesearch)

from Figure 10 the improvement in the PAPR is about 06 dBat the CCDF value of 10minus3 compared to the value of 04 dB inFigure 9 Figure 11 shows the histogram of the index of thedummy symbol selected in the simulation result of Figure 10It is interesting to observe that 4 of the possible values of thedummy sequence are selected with much higher probabilitycompared to the other 12 values This result may providefurther insight into the selection of the dummy sequence

Similar PAPR improvement is obtained for the case of64 QAM modulation format wherein a reduction of about07 dB is achieved at theCCDF value of 10minus3 when the dummysymbol is varied over all possible 64 values The detailed

0 2 4 6 8 10 12 14 160

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Figure 11 Histogram of the dummy symbol index selected in thesimulation example of Figure 10

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Figure 12 Histogram of the dummy symbol index selected for thecase of 64 QAMmodulation

graph for the CCDF for this case is not included for the sakeof brevity however the histogram of the selected symbol isshown in Figure 12 Examination of Figure 12 again showsthe interesting result that the histogram has sharp peaks atfour of the 64 possible values in the constellation diagramInterestingly this result is very similar to that of Figure 11Thus it is possible to reduce the number of trials for thedummy symbol to 4 without any significant degradation inperformance This in fact is done in some of the simulationspresented latter in the paper

Another technique used for the reduction of the peak toaverage power reduction consists of precoding the modula-tion symbol vector by a transform matrix The simulationresults are presented next to evaluate the PAPR performancewith the precoding techniques The simulation results whenboth the precoding and dummy sequence are used simulta-neously are presented as well


Table 1 PAPR Improvement in dB at CCDF of 10minus3 for the precoding DSI and the hybrid precoding-DSI methods (PAPR = 10 dB forstandard OFDM)

16 QAM 64 QAM

Number of recursions Improvement in PAPR (dB) Number of recursions Improvement inPAPR (dB)

OFDM 1 mdash 1 mdashWHT 1 107 1 094DCT 1 184 1 180DHT 1 370 1 304DSI (119881119879 = 04) 869 039 1441 048DSI (All) 16 064 64 078WHT-DSI (119881119879 = 01) 841 111 4449

(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117

WHT-DSI (All) 16 130 64 141DCT-DSI (119881119879 = 01) 809 196 1664 177DCT-DSI (119881119879 = 02) 1336 209 mdash mdashDCT-DSI (All) 16 213 64 190DHT-DSI (119881119879 = 006) 723 378 1658 316DHT-DSI (119881119879 = 008) 1021 379 mdash mdashDHT-DSI (All) 16 381 64 318

2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDMOFDM-Pc (DFT)OFDM-Pc (DHT)

OFDM-Pc (DCT)OFDM-Pc (WHT)

Figure 13 Comparison of the CCDF of the peak to average powerratio with different precoding matrices

Figure 13 plots the CCDF of the PAPR for the 16 QAMmodulation and 64 subcarriers case when the precodingtechnique is used Three different precoding matrices of thepublished literature namely the discrete Hartley transform(DHT) discrete cosine transform (DCT) and the Walsh-Hadamard transform (WHT) matrices are considered forthe simulations In Figure 13 and subsequent figures theabbreviation Pc stands for precodingThus OFDM-Pc(DHT)denotes the case of the OFDM system with precoding based

on the discreteHartley transformThefigure also includes thecase of using the DFT transform for precoding which reducesthe OFDM system to a single carrier system

As may be inferred from Figure 13 the discrete Hartleytransform provides the best performance among the threetransforms with a reduction of 37 dB in PAPR at CCDFof 10minus3 with the DCT and WHT providing a reduction of184 dB and 107 dB respectively The results obtained for theprecodingmethod theDSImethod and the hybrid precodingplus DSI (Pc-DSI) method are summarized in Table 1 interms of the reduction in the PAPR at the CCDF valueof 10minus3 for these methods The results in Table 1 includeboth methods of selecting the optimum dummy symbolIn the first method the search is continued until the PAPRimprovement exceeds certain specified threshold 119881119879 selectedto be 01 dB and 02 dB in the table In the second methodall possible 119872 symbols are tried in selecting the optimumdummy symbol The results for the two cases of 119872 = 16and119872 = 64 are included in the table The table also includesthe average number of recursions for the case of DSI and thehybrid Pc-DSI methods In terms of a direct implementationone recursion for the case of precoding techniques involves 1matrix vector multiplication and 1 119873-point IFFT operationFor the case of DSI it involves one IFFT operation and forthe hybrid Pc-DSI method one recursion involves 1 matrixvector multiplication and 1 119873-point IFFT operation Thecomputational requirements may be reduced by appropriatereorganization of the computations as shown in the previoussection of the paper

Examination of Table 1 shows that the precoding methodwith discrete Hartley transform (DHT) provides the bestperformance among the precoding techniques with a PAPRimprovement of 37 dB and 30 dB respectively for the case


Table 2 Indices of the transforms (119873119879 = 16)Index Transform1 I2 DHT3 DCT4 WHT5 DHTlowastDCT6 DHTlowastWHT7 DCTlowastDHT8 DCTlowastWHT9 WHTlowastDHT10 WHTlowastDCT11 DHTlowastDCTlowastWHT12 DHTlowastWHTlowastDCT13 DCTlowastDHTlowastWHT14 DCTlowastWHTlowastDHT15 WHTlowastDHTlowastDCT16 WHTlowastDCTlowastDHT

of119872 equal to 16 and 64 respectively Including the DSI withthe DHT precoding improves the PAPR by an additional 01ndash02 dB Increasing the number of dummy symbols may resultin some marginal increase in performance but at the cost ofhigher computational complexity

Figure 14 shows the CCDF of the PAPR obtained with themultiple transform technique wherein one of the119873119879 possibletransform matrices including the case of no transform isselected to optimize the PAPR in each OFDM frame shownasOFDM-OP (OFDMwith optimum transform) in the figureand compares it with that obtained with the fixed transformmethods Table 2 lists the various transforms used in thesimulations presented in Figure 14

In Figure 14 the number of subcarriers is 64 and 64QAM modulation is considered As may be inferred fromFigure 14 the optimum transform provides an improvementof about 13 dB over the discrete Hartley transform thathas the best performance among all of the fixed transformmethods Figure 15 plots the corresponding result for thecase of 256 QAM modulation showing an improvement ofabout 14 dB compared to the best of the previous schemesThis is remarkable in that the PAPR obtained with the use ofthe optimum transform method is only about 09 dB worsecompared to the single carrier system with a high ordermodulation

Figure 16 shows the histogram of the number of times atransform is optimum and is selected for the PAPR reductionAs may be inferred from the figure the DHT transform isoptimummost often followed by DCT andWHT transformswith the remaining cases occurring with about uniformprobability This may not come as a surprise as amongthe fixed transform methods the DHT provides the bestperformance However it is not the best among all the casesand that is where the performance improvement comes from

Figure 17 shows the simulation result for the optimumtransform method along with the use of one dummy symbol

3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

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PAPR (dB)

100

10minus1

10minus2

10minus3

OFDMOFDM-Pc (DFT)OFDM-Pc (DHT)OFDM-Pc (DCT)

OFDM-Pc (WHT)OFDM-OP (NT = 4)OFDM-OP (NT = 10)OFDM-OP (NT = 16)

Figure 14 Comparison of the CCDF of the PAPR obtained withvarious transform methods (64 QAM)

3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

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PAPR (dB)

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10minus1

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10minus3




along with the result obtained with the fixed transformmethods for reference As an interesting case Figure 16 alsoincludes the case wherein the transform selection is limitedto only four cases namely DFT that is equivalent to singlecarrier case WHT DCT and the DHT The case of hybridDHT-DSI has already been considered inTable 1 showing thatthe marginal improvement due to DSI when used with theDHT is limited to about 01 dB and is not included in Figure 17for clarity As may be inferred from Figure 17 the proposed


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Figure 16 Histogram of the frequency of selection of the varioustransforms

4 6 8 10 12 14 16

CCD

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10minus1

10minus2

10minus3


OFDM-Pc (WHT)OFDM-OP-DSI (NT = 4ND = 1)OFDM-OP-DSI (NT = 10 ND = 1)OFDM-OP-DSI (NT = 16ND = 1)

Figure 17 PAPR performance of the OFDM-OP-DSI method incomparison with the other methods

OFDM-OP-DSI method provides an improvement of about175 dB in PAPR over the DHT method and what is perhapseven more remarkable is the fact that it is only about 045 dBworse compared to case of a single carrier It is interesting tonote that when the transform selection is limited to only 4cases mentioned earlier the improvement is only about onehalf of that with the full selection of the 16 transforms Thusit is the combination of the wide selection of the transformsalong with the dummy symbol that provides the maximumreduction in the PAPR The histogram of the frequency ofselection of the various transforms is very similar to that inFigure 16 and is not presented here

0 10 20 30 40 50 600

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Figure 18 Histogram of the symbol frequency for the optimumtransform method

The results in Figure 17 are obtained when the dummysymbol is selected optimally by an exhaustive search There-fore it is of interest to find if there is any specific patternin the selection of the dummy symbol Figure 18 shows thehistogram of the dummy symbol selection frequency forthe case of the OFDM-OP-DSI method As may be inferredfrom the figure the histogram shows four distinct peaks thatcorrespond to the boundary symbols 0 7 56 and 63 shownin the signal constellation diagram of Figure 8

When the selection of the dummy symbol is restrictedto one of the four symbols 0 7 56 63 with the highestfrequencies in the histogram of Figure 18 the performancein terms of PAPR is very close to that obtained in Figure 17Figure 19 plots the PAPR result for the multitransform-DSIcase on an expanded scale when the number of transforms119873119879 is equal to 16 and wherein 119873119882 denotes the number ofsymbols in the signal constellation over which the dummysymbol is optimized As may be inferred for the figure for aCCDF value of 10minus3 the PAPR is equal to about 525 dB with119873119882 = 64 For the case wherein the selection of the dummysymbol is restricted to 119873119882 = 4 symbols the correspondingvalue of PAPR is about 01 dB higher Thus with only arelatively very small increase in the PAPR the computationalcomplexity can be reduced by an order of magnitude Inanother alternative method the dummy symbol is selectedon the basis of a threshold on the PAPR In this method forthe selected symbol the PAPR is evaluated and comparedwith the PAPR evaluated for the standard OFDM for thesame OFDM frame If the PAPR for the multitransform-DSImethod exceeds the threshold the search is discontinuedotherwise another dummy symbol is tried The threshold isequal to PAPR value predicted for the multitransform-DSImethod at the CCDF value read from the CCDF versus PAPRgraph for the OFDM method at the computed PAPR valuefor the OFDMmethodminus the specified value of119881119879 In thethresholdmethod first the symbols in the set 0 7 56 63 areselected followed by selection of other symbols in the signalconstellation Figure 19 shows the PAPR performance for the


Table 3 PAPR of the OFDM-OP-DSI method for the reduction in PAPR (64 QAM 64 FFT)

Parameters of the PAPR reduction method PAPR (dB) Reduction in PAPR (dB) ΔPAPRStandard OFDM 10 mdash119873119879 = 3119873119882 = 64 622 378 146119873119879 = 12119873119882 = 64 554 446 078119873119879 = 16119873119882 = 64 525 475 049119873119879 = 3119873119882 = 4 625 375 149119873119879 = 12119873119882 = 4 582 418 106119873119879 = 16119873119882 = 4 530 470 055Single carrier system 476 mdash 0

35 4 45 5 55 6 65 7 75

CCDF plots of PAPR 64pt FFT (64 QAM)

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

ThresholdOFDM-OP-DSI (NW = 4)

OFDM-OP-DSI (NW = 64)OFDM-OP-DSI (NW = 64 Thr)

Figure 19 PAPR performance of the OFDM-OP-DSI method (119873119879= 16)

multitransform-DSI thresholdmethod for both119873119882 = 64 and119873119882 = 4 As may be inferred from Figure 19 the performancefor the threshold case with119873119882 = 64 is about the same as forthe case of exhaustive search with119873119882 = 4

Table 3 summarizes the PAPR at a CCDF value of10minus3 for the OFDM-OP-DSI method wherein 119873119882 denotesthe number of possible symbols over which the dummysymbol selection is optimized and 119873119879 is number of possibletransformsThe table includes the case of single carrier trans-mission for comparison and also lists the ΔPAPR defined asthe difference between the PAPR achieved with the OFDM-OP-DSI method and that of the single carrier transmission atthe CCDF value of 10minus3

As may be inferred from Table 3 the OFDM-OP-DSIsystem with119873119879 = 12 provides an improvement of 446 dB inPAPR over the OFDM with the resulting PAPR only 078 dBhigher than for the single carrier transmission With 119873119879 =16 the improvement is 475 dB in PAPR over the OFDMwith the resulting PAPR only 049 dB higher than for thesingle carrier transmission thus almost entirely eliminatingthe PAPR limitation of the OFDM system It may be possible

52 subcarriers

Pilot tones

Figure 20 Subcarrier layout for IEEE OFDM standard (64 subcar-riers)

to reduce this gap of 049 dB further by increasing the numberof dummy symbols to more than 1 andor by increasingthe number of total transforms beyond 16 considered inthe paper at the expense of some additional computationsOn the other hand the computational complexity can besignificantly reduced by restricting the number of symbols119873119882 from which the dummy symbol is selected at the costof some increase in the PAPR As shown in the table with119873119882 = 4 and 119873119879 = 16 the PAPR reduction is 470 dBcompared to 475 dB with119873119882 = 64 For the case of119873119879 = 12and 119873119882 = 4 the PAPR reduction is 418 dB compared to446 dB with 119873119882 = 64 thus resulting in a relatively smalldegradation in PAPRdue to the reduction in119873119882 from64 to 4However the reduction in119873119882 from64 to 4 results in an orderof magnitude reduction in the computational requirementsThus the OFDM-OP-DSI method provides a PAPR that isonly about 05 dB worse than for the single carrier systemwith only moderate computational requirements This gap ofabout 05 dBmay be further reduced by selecting the numberof transforms119873119879 to be higher than 16

51 Results for the Case of IEEE 80211 Standard The simu-lation results presented thus far are for the ideal case whenall of the 119873 subcarriers are used for transmission includingthose allocated to the dummy symbols and the transformindices However in various OFDM standards some of thesubcarriers near the band edge are not used for transmissionin order to minimize the degradation due to the taperingin the frequency response of the band limiting transmissionfilter For example as shown in Figure 20 in the IEEE 80211standard with 119873 = 64 only 52 subcarriers are used fortransmission with 12 subcarriers not used for transmissionOut of the 52 subcarriers used for transmission 4 of these arefor pilot tones with 48 used for data transmission


3 4 5 6 7 8 9 10 11 12 13 14

OFDMOFDM-Pc (DHT)OFDM-Pc (DCT)OFDM-Pc (WHT)

CCDF plots of PAPR 64pt FFT (M-ary QAM)

Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)

OFDM-OP [NT = 4]OFDM-OP [NT = 10]

OFDM-OP [NT = 16]

Figure 21 Comparison of the CCDF of the PAPR obtained withvarious transform methods (IEEE standard 64 QAM)

Figure 21 plots the result for the complementary cumu-lative distribution function (CCDF) of the paper for varioustransform techniques including the multitransform methodof the paperwith the use of 48-point orthonormal transforms

Comparison of Figure 21 with Figure 14 shows that forthe case of multitransform method there is no significantdifference in performance between the ideal case of 64 pointtransform and the 48-point transform except that for thecase of 119873119879 = 4 48-point transform the PAPR is about04 dB higher compared to the case of 119873119879 = 4 64-pointtransform at the CCDF value of 10minus3 Such a result mayalso be intuitively expected However similar comparisonfor the fixed transforms case shows a drastic differencein performance For example for the DHT transform thePAPR value for the case of 48-point transform case is about92 dB compared to the value of about 72 dB for the 64-point transform case showing that being with some of thesubcarriers with no transmission reduces the effectivenessof the fixed DHT orthonormal transform The result forthe case of DCT and WHT transforms is not as drastichowever the improvement in PAPR with either of thesetransforms is relatively small in both of the 48-point and 64-point transform cases As may be inferred from Figure 21for the 48-point case relevant to the IEEE standard themultitransform method provides an improvement of about36 dB over the best fixed transformmethod at a CCDF valueof 10minus3

Figure 22 plots the CCDF of the PAPR obtained withthe composite transform and dummy symbol insertion (DSI)methods with 119873119863 = 1 for the case of IEEE standard 48-point transform Comparison of Figure 22 shows that theresults obtained are very similar to that obtained for the

4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)

OFDM-Pc (DHT)OFDM-Pc (DCT)OFDM-Pc (WHT)

OFDM-OP-DSI [NT = 4ND = 1]OFDM-OP-DSI [NT = 10 ND = 1]

OFDM-OP-DSI [NT = 16ND = 1]

Figure 22 PAPR performance of the OFDM-OP-DSI method incomparison with the other methods (IEEE standard 64 QAM)

transform methods in Figure 21 For the multitransform theDSI reduces the PAPR to about 54 dB compared to the valueof about 59 dB obtained without DSI for the case of 11987311987916 However for the case of fixed transform there is nosignificant improvement in the PAPR due to the use of asingle dummy symbol Simulation results with119873119863 = 2 showthat the multitransform method with DSI provides a PAPRvalue of about 49 dB with119873119879 = 16 at a CCDF value of 10minus3In comparison there is no appreciable improvement for thefixed transform methods with 119873119863 = 2 When the search forthe dummy symbols is restricted to the 4 boundary symbolsgiven by 0 7 56 63 in the constellation diagram of Figure 8there is only a minor degradation of about 01 dB in the PAPRreduction

6 Conclusions

The paper has presented multitransform methods and sys-tems taught in US Patent 8995542 March 31 2015 for thereduction of peak to average power ratio (PAPR) in OFDMsystems Simulation results on the performance of variousPAPR reduction techniques for the OFDM systems arepresented Detailed simulation results have been presentedon the comparison of the performance of various fixedprecoding transform techniques and the multitransformtechnique with and without the dummy symbol insertion(DSI) techniques

The fixed transform techniques include the discrete Hart-ley transform (DHT) Walsh-Hadamard transform (WHT)and discrete cosine transform (DCT) The transform tech-niques with or without DSI have a reasonable computa-tional requirement do not introduce any distortion andmay


introduce relatively small decrease in the bandwidth effi-ciency In fact the recently inventedmultitransform-DSI tech-niques need only 1 or 2 dummy symbols to obtain optimumperformance and thus possess high bandwidth efficiency aswell

In terms of the dummy symbol insertion method thedummy symbol selection is made by an exhaustive opti-mization over the constellation diagram of the modulatedsymbols It is observed that in the simulated examples theoptimum symbol belongs to a small subset of four symbolswith a probability close to 1 Thus in actual implementationthe selection of the dummy symbol may be confined to sucha subset resulting in significant reduction in computationaleffort without causing any significant reduction in the PAPRperformance compared to the case wherein the selection ismade from the complete symbol constellation

The simulation results have been presented for twogeneral cases In the first of these cases all of the OFDMchannels are included in the transform operation In thesecond case applicable to the IEEE 80211 standard only asubset of the OFDM channels is included in the transformoperation with either the remaining channels carrying zerosor the pilot symbols The pilot symbols are not includedin the transform operation for ease of subcarrier frequencysynchronization although synchronization methods may bedevised for the first case as well

Simulation results show that among the fixed transformmethods the DHT method provides the best performanceFor example for the case where all the channels are includedin the transformoperation andwith 64QAMmodulation theDHT method provides a PAPR of about 7 dB correspondingto a CCDF of 10minus3 or with a probability of 0999 with thecorresponding values of the PAPR for the DCT and WHTequal to about 87 dB and 93 dB respectively For the multi-transform technique with 119873119879 equal to 16 the value of PAPRis about 58 dB providing an improvement of 12 dB overthe best fixed transform Similar results are obtained forother modulation schemes Similar differences in PAPR forvarious fixed and multitransform methods are observed forthe case of 256 QAM The multicarrier penalty in terms ofincreased PAPR is reduced to only 08 dB with the use ofthe multitransform technique and represents a reduction ofabout 45 dB compared to the original OFDM without anyprecoding transform

In terms of the composite transform-DSI techniqueinsertion of 1 or 2 dummy symbols selected optimallyfrom the symbol constellation diagram shows no significantchange for the fixed transform methods However the PAPRfor the multitransform-DSI method with just 1 dummysymbol is just 05 dB higher compared to the single carriertransmissionThis difference can be further reduced to nearly0 with an increase in the value of 119873119879 and the number ofdummy symbols119873119863

The difference between the fixed transform and multi-transform methods becomes even more pronounced whenonly a subset of the OFDM channels are included in thetransform For example for the IEEE 80211 standard with64 OFDM channels 11 of the OFDM channels carry zeros

and 48 of the channels are used for data using a 48-pointprecoding transform For this case the simulation resultsshow that for 64 QAM the multitransform-DSI method with119873119879 = 16 and the number of dummy symbols 119873119863 = 1provides a PAPR value of 54 dB that is reduced to about50 dB with 119873119863 = 2 and is equal to that obtained forthe single carrier transmission thus eliminating any PAPRpenalty of the multicarrier OFDM system In contrast to thisfor exactly the same simulation conditions the PAPR of thefixed transform methods is equal to about 92 dB Limitingthe dummy symbol search to the optimal subset of 4 symbolsof the constellation diagram does not result in any significantPAPR performance difference

Disclosure

The material in this paper is protected under US Patent8995542 March 31 2015

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R Van Nee and R Prasad OFDM for Wireless MultimediaCommunications Artech House Norwood Mass USA 2000

[2] J R Simic ldquoAnalysis of OFDM multiuser system over fadingchannelsrdquo in Proceedings of the 5th International Conference onTelecommunications inModern Satellite Cable and BroadcastingService (TELSIKS rsquo01) Nis Yugoslavia September 2001

[3] A R S Bahai and B R Saltzberg Multi-Carrier DigitalCommunications Theory and Applications of OFDM KluwerAcademicPlenum Publishers 1999

[4] J Heiskala and J TerryOFDMWireless LANs ATheoretical andPractical Guide Sams Publishing Indianapolis Ind USA 2002

[5] M D Benedetto and G Giancola Understanding Ultra WideBand Radio Fundamentals Prentice Hall New York NY USA2004

[6] IEEE Standard ldquoPart 11 wireless LANMedium Access Control(MAC) and Physical Layer (PHY) specifications high-speedphysical layer in the 5GHZ bandrdquo IEEE Standard 80211a 1999

[7] R Kumar and M Khan ldquoMitigation of multipath effects inbroadband wireless systems using quantized state adaptiveequalization methodrdquo in Proceedings of the IEEE AerospaceEngineering Conference pp 1ndash9 Big Sky Mont USA March2006

[8] R Kumar ldquoA higher-order analysis of the distortion effects ofnonlinera amplifiers on CDMA signalsrdquo in Proceedings of theIEEE Aerospace Engineering Conference pp 1ndash10 Big SkyMontUSA March 2008

[9] R Kumar ldquoAdaptive Compensation Systems forMitigatingDis-tortion due to Nonlinear Power Amplifiersrdquo Patent ApplicationUS 20110234314 2011

[10] R Kumar ldquoSystems and Methods for Mitigating SpectralRegrowth from Nonlinear Systemsrdquo Patent Application US2012 0280749 November 2012


[11] R Kumar ldquoMulti Transform OFDM systems and Methodswith Low Peak to Average Power Ratio Signalsrdquo U S Patent8995542 March 2015

[12] L Wang and C Tellambura ldquoA simplified clipping and filteringtechnique for PAR reduction in OFDM systemsrdquo IEEE SignalProcessing Letters vol 12 no 6 pp 453ndash456 2005

[13] R W Bauml R F H Fischer and J B Huber ldquoReducingthe peak-to-average power ratio of multicarrier modulation byselected mappingrdquo Electronics Letters vol 32 no 22 pp 2056ndash2057 1996

[14] S H Muller and J B Huber ldquoOFDM with reduced peak-to-average power ratio by optimum combination of partialtransmit sequencesrdquo Electronics Letters vol 33 no 5 pp 368ndash369 1997

[15] S H Muller and J B Huber ldquoA comparison of peak powerreduction schemes for OFDMrdquo in Proceedings of the IEEEGlobal Communication Conference (GLOBECOM rsquo07) pp 1ndash5November 1997

[16] H-G Ryu J-E Lee and J-S Park ldquoDummy Sequence Inser-tion (DSI) for PAPR reduction in the OFDM communicationsystemrdquo IEEE Transactions on Consumer Electronics vol 50 no1 pp 89ndash94 2004

[17] P Van Eetvelt G Wade and M Tomlinson ldquoPeak to averagepower reduction for OFDM schemes by selective scramblingrdquoElectronics Letters vol 32 no 21 pp 1963ndash1964 1996

[18] H Ochiai and H Imai ldquoMDPSK-OFDM with highly powerefficient block codes for frequency-selective faing channelsrdquoIEEE Transactions on Vehicular Technology vol 49 no 1 pp74ndash82 2000

[19] T A Wilkinson and A E Jones ldquoMinimization of the peakto mean envelope power ratio of multicarrier transmissionschemes by block codingrdquo in Proceedings of the IEEE 45thVehicular Technology Conference pp 825ndash829 Chicago IllUSA July 1995

[20] A E Jones T A Wilkinson and S K Barton ldquoBlock codingscheme for reduction of peak to mean envelope power ratio ofmulticarrier transmission schemesrdquo IEE Electronic Letters vol30 no 25 pp 2098ndash2099 1994

[21] I Baig and V Jeoti ldquoPAPR analysis of DHT-precoded OFDMsystem for M-QAMrdquo in Proceedings of the International Confer-ence on Intelligent and Advanced Systems (ICIAS rsquo10) pp 1ndash4Kuala Lumpur Malaysia June 2010

[22] V Jeoti and I Baig ldquoDCT precoded SLM technique for PAPRreduction inOFDM systemsrdquo in Proceedings of the InternationalConference on Intelligent and Advanced systems (ICIAS rsquo10) pp1ndash6 June 2010

[23] S-W Kim J-K Chung and H-G Ryu ldquoPAPR reduction ofthe OFDM signal by the SLM-based WHT and DSI methodrdquoin Proceedings of the IEEE Region 10 Conference (TENCON rsquo06)pp 1ndash4 IEEE Hong Kong November 2006

[24] R Van Nee and A De Wild ldquoReducing the peak-to-averagepower ratio ofOFDMrdquo inProceedings of the 48th IEEEVehicularTechnology Conference (VTC rsquo98) vol 3 pp 2072ndash2076OttawaCanada May 1998

[25] J-C Wu C-M Li and C-C Tseng ldquoA PDSI with STBCscheme for PAPR reduction in OFDM systemrdquo in Proceedingsof the International Conference on Consumer Electronics Com-munications and Networks (CECNet rsquo11) pp 3851ndash3854 IEEEXianning China April 2011

[26] C Oestges and B Clerckx MIMI Wireless CommunicationsAcademic Press 2007

[27] A B Gershman and N D Sidiropoulos Space-Time Processingfor MIMO Communications John Wiley amp Sons 2005

[28] L L Hanzo Y Akhtman LiWang andM JiangMIMI-OFDMfor LTE WiFi and WiMAX John Wiley amp Sons New York NYUSA 2011

[29] Y Tadokoro and T Higuchi ldquoDiscrete Fourier transformcomputation via the Walsh transformrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 26 no 3 pp 236ndash240 1978

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design



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Civil EngineeringAdvances in

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Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Serialto

parallelconvertor

(SP)

Parallelto

serialconvertor

(PS)

Inversefast

Fouriertransform

(IFFT)

Inputdata

Basebandmodulator

Guardinterval

insertionblock

Bandlimiting

filterCarrier

modulatord(k) s(k)

X1(k)

X2(k)

XN(k)

x1(k)

x2(k)

xN(k)

OFDMsignal(t)gs(t)gs(n) gse(n)

Figure 1 Block diagram of the OFDM system

The contents of the paper are organized as followsSection 2 of the paper presents a brief introduction to theOFDM system along with various notations used in thepaper Section 3 provides a brief review of the various peakto average power ratio (PAPR) reduction techniques in thepublished literature Section 4 presents multitransform sys-tems and methods recently invented by the first author ofthe paper and taught in US Patent 8995542 March 2015[11] for an effective PAPR reduction which have a reasonablecomputational requirement do not introduce any distortionneed relatively insignificant decrease in the bandwidth effi-ciency and provide PAPR very close to that for the singlecarrier modulation systems thus effectively eliminating anyPAPR penalty incurred by the multicarrier OFDM systemSection 5 presents simulation results on the performance ofthe various PAPR reduction techniques Section 6 presentssome concluding remarks

2 OFDM System

An OFDM-modulated signal consists of the parallel trans-mission of several signals that are modulated at differentcarrier frequencies evenly spaced by Δ119891 [1ndash7] The complexvalued input symbol sequence 119904(119895) is split into 119873 subse-quences 119904119898(119896) with 119904119898(119896) = 119904(119899) 119899 = 119896119873 + 119898 119898 =0 1 119873 minus 1 119896 = 0 1 2 The symbol subsequence119904119898(119896) modulates a corresponding subcarrier at frequency119891119898 for 119898 = 0 1 119873 minus 1 Thus the time sampled versionof the complex envelope 119892119904(119899) of the modulated signal isgiven by (1) wherein the sampling period 119879119878 = 1198790119873 with1198790 denoting the symbol period for the subsequence 119904119898(119895)119892119904 (119899 + 119896119873) = 1radic119873

119873minus1sum119898=0

119904119898 (119896) exp [1198952120587119898119899119873 ] 119899 = 0 1 119873 minus 1 119896 = 0 1

(1)

The consecutive 119873 samples of 119892119904(119899) constitute an OFDMsymbol and according to (1) the samples during the 119896thOFDM symbol may be obtained by an119873 point IFFT (inversefast Fourier transform) of the consecutive 119873 symbols in thesymbol sequence 119904(119895) or the 119896th symbols in the symbolsubsequences 119904119898(119896) 119898 = 0 1 (119873 minus 1) In the multipleaccess application of OFDM the symbol subsequence 119904119898(119896)may be the symbol sequences generated for the 119873 multipleaccess users rather than subsequences of a single user symbol

sequence The OFDM signal has a guard interval of length119879119866 for each OFDM symbol to mitigate the intersymbolinterference The sample values during any guard intervalare obtained by the periodic extension of the subsequent 119873sample values of 119892119904(119899) The transmitted radio frequency (RF)OFDM signal V(119905) is given by

V (119905) = Re 119892119904 (119905) exp [1198952120587119891119888119905] (2)

where 119891119888 denotes the carrier frequency and 119892119904(119905) denotesthe continuous time signal obtained by interpolation of thesampled signal 119892119904(119899) using for example 0th order hold Thesignal 119892119904(119899)may also be band limited by a band limiting filtersuch as the square root raised cosine filter in generating theanalog signal 119892119904(119905)

Figure 1 shows the block diagram of the OFDM sys-tem Referring to Figure 1 the data 119889(119896) that may be abinary stream is inputted to the baseband modulator blockthat modulates the input data according to a modulationscheme that is selected to be the QAM modulation Theresults of the paper will apply equally well to various othermodulation techniques such as MPSK or MASK modulationschemes The complex baseband signal 119904(119896) 119896 = 0 1 isinputted to the serial to parallel converter with the outputgiven by the OFDM modulation symbol vector 119883(119896) =[1198831(119896) 1198832(119896) sdot sdot sdot 119883119873(119896)]119879 where 119883119898(119896) = 119904119898(119896) or119883119898(119896) = 119904(119899) 119899 = 119896119873 + 119898 119898 = 0 1 119873 minus 1119896 = 0 1 The inverse fast Fourier transform (IFFT) blockprovides the inverse Fourier transform of 119883(119896) providingthe OFDM modulated signal vector 119909(119896) of dimension 119873also referred to as the OFDM frame at the output that isinputted to the parallel to serial converter block The parallelto serial converter block concatenates the components 119909119898(119896)of the vector119909(119896)providing the basebandOFDMsignal119892119904(119899)119899 = 119896119873 + 119898 given by (1) The complex baseband OFDMsignal 119892119904(119899) is inputted into the guard band insert block forextending the OFDM signal duration by the guard interval119879119866 by a periodic extension of the signal 119892119904(119899) The OFDMbaseband signal with a guard interval denoted by 119892119904119890(119899) isinputted to a band limiting filter that may be for examplea square root raised cosine filter and may include a digitalto analog converter providing the filtered complex basebandOFDM signal 119892119904(119905) that modulates a carrier signal providingthe bandpass OFDM signal V(119905) given by (2) This paperis focused upon the subsystem of the OFDM system that





1003816100381610038161003816119892119904 (119905)10038161003816100381610038162119864 [1003816100381610038161003816119892119904 (119905)10038161003816100381610038162] (3)


PAPR cong max1198991003816100381610038161003816119909119899 (119896)10038161003816100381610038162119909 (119896)2 119873 (4)

















(6)




1198822 = [1 11 minus1]

119898 = 2 3

(8a)

119875119882 = 1radic11987311988221198980 119873 = 21198980 (8b)





SPconverter

IFFT

IFFT

IFFTInput

selector

OFDMsignal

PSconverter

Inputdata

Basebandmodulator

d(k) s(k) X(k)

X1(k)

X2(k)

x1(k)

x2(k)

x(k)

P1

P2gs(n)

PN119879

XN119879(k) xN119879(k)







Fminus1 119883 (119896) = F

minus1 [119883119877 (119896)] + 119895Fminus1 [119883119868 (119896)] (12)



IFFT

DCT IFFT

IFFT

IFFT

X(k) = X1(k)

X1(k)

x1(k)x1(k)

x2(k)

x3(k)

x4(k)

X2(k)

X3(k)

X4(k)

IFFT rarrDHT

IFFT rarrWHT







+

Dummysymbolsvector

generator

+Input

selector

IFFT

IFFT

IFFT

MinimumPAPR

evaluatorYes

No

PSconverter

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

X1(k)

X2(k)

x1(k)

x2(k)

P1

P2

PAPRmltVT

xo(k)

SPconverter

insertionwith 0 s

sumgs(n)

XI(k)

XD(k) PN119879

XN119879(k) xN119879(k)





119909119899 (119896) = 119875119865119875119899119883(119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119883119863 (119896) (14a)


119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119878119910119863 (119896)= 119875119865119875119899119883119868 (119896) + 119875119899119863119910119863 (119896) (14b)


119875119899119878 = [1198751198991198951 1198751198991198952 sdot sdot sdot 119875119899119895119873119879 ] (15)


119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119901119899119904119863 (119896) (16)




+

+

Dummysymbols

subvectorgenerator

IFFT

IFFT

IFFT

Yes

No

PSconverter

+

+

++

+

++

Inputselector

MinimumPAPR

evaluator

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

P1

P2

PAPRm

xo(k)

SPconverter

insertionwith 0 s

q1

q2

qNT

times

times

times

ltVT

sum

sum

sum

gs(n)

XI(k)

PN119879

xN119879(k)

P1D

P2D

PN119879D

yD(k)

XI1(k)

XI2(k)

XIN119879(k)

xI1(k)

xI2(k)

xIN119879(k)






119902119899 = 1198751198651198751198991 119904119899119894 (17)


119909119899 (119896) = 119909119868119899 (119896) + 119901119899 (119896) + 119902119899 (18)




ReceivedOFDM signal



block

SPconverter

FFTblock


Dummyand

indexingdeletion

block

PSconverter

Basebanddemod

xo(k)

d(k)

r(t)

no

Xo(k)

Inversetransform

block(Pn119900 )

gs(n)gse(n)






119903119899 (119896) = 100381610038161003816100381610038161205951198991198671198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 = 100381610038161003816100381610038161198751198991198671 1198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 119899 = 1 2 119873119879

(19)


119903119899 (119896) = 100381610038161003816100381610038161198751198991198671 11987511989901 1199041198990119894 + 119894119904 minus 119904119899119894 100381610038161003816100381610038162 119899 = 1198990 1199031198990 = 0 (20)




119875119899 = [[1 00119879 119875119899]]

(21)


min119899

100381610038161003816100381611988311989901 minus 119904119899119894 10038161003816100381610038162 = min119899

10038161003816100381610038161199041198990119894 + 120585 (119896) minus 119904119899119894 10038161003816100381610038162 (22)





Im

Re

0 4 8 12

13951

2 6 10 14

1573 11


0

1

2

3

8 16 24 32 40 48 56

10 18 26 34 42 50 58

9 25 41 5717 33 49

11 27 43 5919 35 51

4

5

6

7

12 20 28

14 22 30

13 2921

15 3123

36

37

38

39

44 52 60

46 54 62

45 6153

47 6355

Im

Re

d





2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)


2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)




0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y


0 10 20 30 40 50 600

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y






16 QAM 64 QAM



(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117


2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













1003816100381610038161003816119892119904 (119905)10038161003816100381610038162119864 [1003816100381610038161003816119892119904 (119905)10038161003816100381610038162] (3)


PAPR cong max1198991003816100381610038161003816119909119899 (119896)10038161003816100381610038162119909 (119896)2 119873 (4)

















(6)




1198822 = [1 11 minus1]

119898 = 2 3

(8a)

119875119882 = 1radic11987311988221198980 119873 = 21198980 (8b)





SPconverter

IFFT

IFFT

IFFTInput

selector

OFDMsignal

PSconverter

Inputdata

Basebandmodulator

d(k) s(k) X(k)

X1(k)

X2(k)

x1(k)

x2(k)

x(k)

P1

P2gs(n)

PN119879

XN119879(k) xN119879(k)







Fminus1 119883 (119896) = F

minus1 [119883119877 (119896)] + 119895Fminus1 [119883119868 (119896)] (12)



IFFT

DCT IFFT

IFFT

IFFT

X(k) = X1(k)

X1(k)

x1(k)x1(k)

x2(k)

x3(k)

x4(k)

X2(k)

X3(k)

X4(k)

IFFT rarrDHT

IFFT rarrWHT







+

Dummysymbolsvector

generator

+Input

selector

IFFT

IFFT

IFFT

MinimumPAPR

evaluatorYes

No

PSconverter

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

X1(k)

X2(k)

x1(k)

x2(k)

P1

P2

PAPRmltVT

xo(k)

SPconverter

insertionwith 0 s

sumgs(n)

XI(k)

XD(k) PN119879

XN119879(k) xN119879(k)





119909119899 (119896) = 119875119865119875119899119883(119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119883119863 (119896) (14a)


119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119878119910119863 (119896)= 119875119865119875119899119883119868 (119896) + 119875119899119863119910119863 (119896) (14b)


119875119899119878 = [1198751198991198951 1198751198991198952 sdot sdot sdot 119875119899119895119873119879 ] (15)


119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119901119899119904119863 (119896) (16)




+

+

Dummysymbols

subvectorgenerator

IFFT

IFFT

IFFT

Yes

No

PSconverter

+

+

++

+

++

Inputselector

MinimumPAPR

evaluator

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

P1

P2

PAPRm

xo(k)

SPconverter

insertionwith 0 s

q1

q2

qNT

times

times

times

ltVT

sum

sum

sum

gs(n)

XI(k)

PN119879

xN119879(k)

P1D

P2D

PN119879D

yD(k)

XI1(k)

XI2(k)

XIN119879(k)

xI1(k)

xI2(k)

xIN119879(k)






119902119899 = 1198751198651198751198991 119904119899119894 (17)


119909119899 (119896) = 119909119868119899 (119896) + 119901119899 (119896) + 119902119899 (18)




ReceivedOFDM signal



block

SPconverter

FFTblock


Dummyand

indexingdeletion

block

PSconverter

Basebanddemod

xo(k)

d(k)

r(t)

no

Xo(k)

Inversetransform

block(Pn119900 )

gs(n)gse(n)






119903119899 (119896) = 100381610038161003816100381610038161205951198991198671198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 = 100381610038161003816100381610038161198751198991198671 1198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 119899 = 1 2 119873119879

(19)


119903119899 (119896) = 100381610038161003816100381610038161198751198991198671 11987511989901 1199041198990119894 + 119894119904 minus 119904119899119894 100381610038161003816100381610038162 119899 = 1198990 1199031198990 = 0 (20)




119875119899 = [[1 00119879 119875119899]]

(21)


min119899

100381610038161003816100381611988311989901 minus 119904119899119894 10038161003816100381610038162 = min119899

10038161003816100381610038161199041198990119894 + 120585 (119896) minus 119904119899119894 10038161003816100381610038162 (22)





Im

Re

0 4 8 12

13951

2 6 10 14

1573 11


0

1

2

3

8 16 24 32 40 48 56

10 18 26 34 42 50 58

9 25 41 5717 33 49

11 27 43 5919 35 51

4

5

6

7

12 20 28

14 22 30

13 2921

15 3123

36

37

38

39

44 52 60

46 54 62

45 6153

47 6355

Im

Re

d





2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)


2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)




0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y


0 10 20 30 40 50 600

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y






16 QAM 64 QAM



(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117


2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















(6)




1198822 = [1 11 minus1]

119898 = 2 3

(8a)

119875119882 = 1radic11987311988221198980 119873 = 21198980 (8b)





SPconverter

IFFT

IFFT

IFFTInput

selector

OFDMsignal

PSconverter

Inputdata

Basebandmodulator

d(k) s(k) X(k)

X1(k)

X2(k)

x1(k)

x2(k)

x(k)

P1

P2gs(n)

PN119879

XN119879(k) xN119879(k)







Fminus1 119883 (119896) = F

minus1 [119883119877 (119896)] + 119895Fminus1 [119883119868 (119896)] (12)



IFFT

DCT IFFT

IFFT

IFFT

X(k) = X1(k)

X1(k)

x1(k)x1(k)

x2(k)

x3(k)

x4(k)

X2(k)

X3(k)

X4(k)

IFFT rarrDHT

IFFT rarrWHT







+

Dummysymbolsvector

generator

+Input

selector

IFFT

IFFT

IFFT

MinimumPAPR

evaluatorYes

No

PSconverter

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

X1(k)

X2(k)

x1(k)

x2(k)

P1

P2

PAPRmltVT

xo(k)

SPconverter

insertionwith 0 s

sumgs(n)

XI(k)

XD(k) PN119879

XN119879(k) xN119879(k)





119909119899 (119896) = 119875119865119875119899119883(119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119883119863 (119896) (14a)


119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119878119910119863 (119896)= 119875119865119875119899119883119868 (119896) + 119875119899119863119910119863 (119896) (14b)


119875119899119878 = [1198751198991198951 1198751198991198952 sdot sdot sdot 119875119899119895119873119879 ] (15)


119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119901119899119904119863 (119896) (16)




+

+

Dummysymbols

subvectorgenerator

IFFT

IFFT

IFFT

Yes

No

PSconverter

+

+

++

+

++

Inputselector

MinimumPAPR

evaluator

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

P1

P2

PAPRm

xo(k)

SPconverter

insertionwith 0 s

q1

q2

qNT

times

times

times

ltVT

sum

sum

sum

gs(n)

XI(k)

PN119879

xN119879(k)

P1D

P2D

PN119879D

yD(k)

XI1(k)

XI2(k)

XIN119879(k)

xI1(k)

xI2(k)

xIN119879(k)






119902119899 = 1198751198651198751198991 119904119899119894 (17)


119909119899 (119896) = 119909119868119899 (119896) + 119901119899 (119896) + 119902119899 (18)




ReceivedOFDM signal



block

SPconverter

FFTblock


Dummyand

indexingdeletion

block

PSconverter

Basebanddemod

xo(k)

d(k)

r(t)

no

Xo(k)

Inversetransform

block(Pn119900 )

gs(n)gse(n)






119903119899 (119896) = 100381610038161003816100381610038161205951198991198671198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 = 100381610038161003816100381610038161198751198991198671 1198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 119899 = 1 2 119873119879

(19)


119903119899 (119896) = 100381610038161003816100381610038161198751198991198671 11987511989901 1199041198990119894 + 119894119904 minus 119904119899119894 100381610038161003816100381610038162 119899 = 1198990 1199031198990 = 0 (20)




119875119899 = [[1 00119879 119875119899]]

(21)


min119899

100381610038161003816100381611988311989901 minus 119904119899119894 10038161003816100381610038162 = min119899

10038161003816100381610038161199041198990119894 + 120585 (119896) minus 119904119899119894 10038161003816100381610038162 (22)





Im

Re

0 4 8 12

13951

2 6 10 14

1573 11


0

1

2

3

8 16 24 32 40 48 56

10 18 26 34 42 50 58

9 25 41 5717 33 49

11 27 43 5919 35 51

4

5

6

7

12 20 28

14 22 30

13 2921

15 3123

36

37

38

39

44 52 60

46 54 62

45 6153

47 6355

Im

Re

d





2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)


2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)




0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y


0 10 20 30 40 50 600

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y






16 QAM 64 QAM



(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117


2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










SPconverter

IFFT

IFFT

IFFTInput

selector

OFDMsignal

PSconverter

Inputdata

Basebandmodulator

d(k) s(k) X(k)

X1(k)

X2(k)

x1(k)

x2(k)

x(k)

P1

P2gs(n)

PN119879

XN119879(k) xN119879(k)







Fminus1 119883 (119896) = F

minus1 [119883119877 (119896)] + 119895Fminus1 [119883119868 (119896)] (12)



IFFT

DCT IFFT

IFFT

IFFT

X(k) = X1(k)

X1(k)

x1(k)x1(k)

x2(k)

x3(k)

x4(k)

X2(k)

X3(k)

X4(k)

IFFT rarrDHT

IFFT rarrWHT







+

Dummysymbolsvector

generator

+Input

selector

IFFT

IFFT

IFFT

MinimumPAPR

evaluatorYes

No

PSconverter

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

X1(k)

X2(k)

x1(k)

x2(k)

P1

P2

PAPRmltVT

xo(k)

SPconverter

insertionwith 0 s

sumgs(n)

XI(k)

XD(k) PN119879

XN119879(k) xN119879(k)





119909119899 (119896) = 119875119865119875119899119883(119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119883119863 (119896) (14a)


119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119878119910119863 (119896)= 119875119865119875119899119883119868 (119896) + 119875119899119863119910119863 (119896) (14b)


119875119899119878 = [1198751198991198951 1198751198991198952 sdot sdot sdot 119875119899119895119873119879 ] (15)


119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119901119899119904119863 (119896) (16)




+

+

Dummysymbols

subvectorgenerator

IFFT

IFFT

IFFT

Yes

No

PSconverter

+

+

++

+

++

Inputselector

MinimumPAPR

evaluator

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

P1

P2

PAPRm

xo(k)

SPconverter

insertionwith 0 s

q1

q2

qNT

times

times

times

ltVT

sum

sum

sum

gs(n)

XI(k)

PN119879

xN119879(k)

P1D

P2D

PN119879D

yD(k)

XI1(k)

XI2(k)

XIN119879(k)

xI1(k)

xI2(k)

xIN119879(k)






119902119899 = 1198751198651198751198991 119904119899119894 (17)


119909119899 (119896) = 119909119868119899 (119896) + 119901119899 (119896) + 119902119899 (18)




ReceivedOFDM signal



block

SPconverter

FFTblock


Dummyand

indexingdeletion

block

PSconverter

Basebanddemod

xo(k)

d(k)

r(t)

no

Xo(k)

Inversetransform

block(Pn119900 )

gs(n)gse(n)






119903119899 (119896) = 100381610038161003816100381610038161205951198991198671198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 = 100381610038161003816100381610038161198751198991198671 1198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 119899 = 1 2 119873119879

(19)


119903119899 (119896) = 100381610038161003816100381610038161198751198991198671 11987511989901 1199041198990119894 + 119894119904 minus 119904119899119894 100381610038161003816100381610038162 119899 = 1198990 1199031198990 = 0 (20)




119875119899 = [[1 00119879 119875119899]]

(21)


min119899

100381610038161003816100381611988311989901 minus 119904119899119894 10038161003816100381610038162 = min119899

10038161003816100381610038161199041198990119894 + 120585 (119896) minus 119904119899119894 10038161003816100381610038162 (22)





Im

Re

0 4 8 12

13951

2 6 10 14

1573 11


0

1

2

3

8 16 24 32 40 48 56

10 18 26 34 42 50 58

9 25 41 5717 33 49

11 27 43 5919 35 51

4

5

6

7

12 20 28

14 22 30

13 2921

15 3123

36

37

38

39

44 52 60

46 54 62

45 6153

47 6355

Im

Re

d





2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)


2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)




0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y


0 10 20 30 40 50 600

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y






16 QAM 64 QAM



(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117


2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










+

Dummysymbolsvector

generator

+Input

selector

IFFT

IFFT

IFFT

MinimumPAPR

evaluatorYes

No

PSconverter

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

X1(k)

X2(k)

x1(k)

x2(k)

P1

P2

PAPRmltVT

xo(k)

SPconverter

insertionwith 0 s

sumgs(n)

XI(k)

XD(k) PN119879

XN119879(k) xN119879(k)





119909119899 (119896) = 119875119865119875119899119883(119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119883119863 (119896) (14a)


119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119875119865119875119899119878119910119863 (119896)= 119875119865119875119899119883119868 (119896) + 119875119899119863119910119863 (119896) (14b)


119875119899119878 = [1198751198991198951 1198751198991198952 sdot sdot sdot 119875119899119895119873119879 ] (15)


119909119899 (119896) = 119875119865119875119899119883119868 (119896) + 119901119899119904119863 (119896) (16)




+

+

Dummysymbols

subvectorgenerator

IFFT

IFFT

IFFT

Yes

No

PSconverter

+

+

++

+

++

Inputselector

MinimumPAPR

evaluator

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

P1

P2

PAPRm

xo(k)

SPconverter

insertionwith 0 s

q1

q2

qNT

times

times

times

ltVT

sum

sum

sum

gs(n)

XI(k)

PN119879

xN119879(k)

P1D

P2D

PN119879D

yD(k)

XI1(k)

XI2(k)

XIN119879(k)

xI1(k)

xI2(k)

xIN119879(k)






119902119899 = 1198751198651198751198991 119904119899119894 (17)


119909119899 (119896) = 119909119868119899 (119896) + 119901119899 (119896) + 119902119899 (18)




ReceivedOFDM signal



block

SPconverter

FFTblock


Dummyand

indexingdeletion

block

PSconverter

Basebanddemod

xo(k)

d(k)

r(t)

no

Xo(k)

Inversetransform

block(Pn119900 )

gs(n)gse(n)






119903119899 (119896) = 100381610038161003816100381610038161205951198991198671198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 = 100381610038161003816100381610038161198751198991198671 1198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 119899 = 1 2 119873119879

(19)


119903119899 (119896) = 100381610038161003816100381610038161198751198991198671 11987511989901 1199041198990119894 + 119894119904 minus 119904119899119894 100381610038161003816100381610038162 119899 = 1198990 1199031198990 = 0 (20)




119875119899 = [[1 00119879 119875119899]]

(21)


min119899

100381610038161003816100381611988311989901 minus 119904119899119894 10038161003816100381610038162 = min119899

10038161003816100381610038161199041198990119894 + 120585 (119896) minus 119904119899119894 10038161003816100381610038162 (22)





Im

Re

0 4 8 12

13951

2 6 10 14

1573 11


0

1

2

3

8 16 24 32 40 48 56

10 18 26 34 42 50 58

9 25 41 5717 33 49

11 27 43 5919 35 51

4

5

6

7

12 20 28

14 22 30

13 2921

15 3123

36

37

38

39

44 52 60

46 54 62

45 6153

47 6355

Im

Re

d





2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)


2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)




0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y


0 10 20 30 40 50 600

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y






16 QAM 64 QAM



(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117


2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










+

+

Dummysymbols

subvectorgenerator

IFFT

IFFT

IFFT

Yes

No

PSconverter

+

+

++

+

++

Inputselector

MinimumPAPR

evaluator

OFDMsignal

Inputdata

Basebandmodulator

d(k) s(k)

P1

P2

PAPRm

xo(k)

SPconverter

insertionwith 0 s

q1

q2

qNT

times

times

times

ltVT

sum

sum

sum

gs(n)

XI(k)

PN119879

xN119879(k)

P1D

P2D

PN119879D

yD(k)

XI1(k)

XI2(k)

XIN119879(k)

xI1(k)

xI2(k)

xIN119879(k)






119902119899 = 1198751198651198751198991 119904119899119894 (17)


119909119899 (119896) = 119909119868119899 (119896) + 119901119899 (119896) + 119902119899 (18)




ReceivedOFDM signal



block

SPconverter

FFTblock


Dummyand

indexingdeletion

block

PSconverter

Basebanddemod

xo(k)

d(k)

r(t)

no

Xo(k)

Inversetransform

block(Pn119900 )

gs(n)gse(n)






119903119899 (119896) = 100381610038161003816100381610038161205951198991198671198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 = 100381610038161003816100381610038161198751198991198671 1198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 119899 = 1 2 119873119879

(19)


119903119899 (119896) = 100381610038161003816100381610038161198751198991198671 11987511989901 1199041198990119894 + 119894119904 minus 119904119899119894 100381610038161003816100381610038162 119899 = 1198990 1199031198990 = 0 (20)




119875119899 = [[1 00119879 119875119899]]

(21)


min119899

100381610038161003816100381611988311989901 minus 119904119899119894 10038161003816100381610038162 = min119899

10038161003816100381610038161199041198990119894 + 120585 (119896) minus 119904119899119894 10038161003816100381610038162 (22)





Im

Re

0 4 8 12

13951

2 6 10 14

1573 11


0

1

2

3

8 16 24 32 40 48 56

10 18 26 34 42 50 58

9 25 41 5717 33 49

11 27 43 5919 35 51

4

5

6

7

12 20 28

14 22 30

13 2921

15 3123

36

37

38

39

44 52 60

46 54 62

45 6153

47 6355

Im

Re

d





2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)


2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)




0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y


0 10 20 30 40 50 600

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y






16 QAM 64 QAM



(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117


2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










ReceivedOFDM signal



block

SPconverter

FFTblock


Dummyand

indexingdeletion

block

PSconverter

Basebanddemod

xo(k)

d(k)

r(t)

no

Xo(k)

Inversetransform

block(Pn119900 )

gs(n)gse(n)






119903119899 (119896) = 100381610038161003816100381610038161205951198991198671198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 = 100381610038161003816100381610038161198751198991198671 1198831198990 (119896) minus 119904119899119894 100381610038161003816100381610038162 119899 = 1 2 119873119879

(19)


119903119899 (119896) = 100381610038161003816100381610038161198751198991198671 11987511989901 1199041198990119894 + 119894119904 minus 119904119899119894 100381610038161003816100381610038162 119899 = 1198990 1199031198990 = 0 (20)




119875119899 = [[1 00119879 119875119899]]

(21)


min119899

100381610038161003816100381611988311989901 minus 119904119899119894 10038161003816100381610038162 = min119899

10038161003816100381610038161199041198990119894 + 120585 (119896) minus 119904119899119894 10038161003816100381610038162 (22)





Im

Re

0 4 8 12

13951

2 6 10 14

1573 11


0

1

2

3

8 16 24 32 40 48 56

10 18 26 34 42 50 58

9 25 41 5717 33 49

11 27 43 5919 35 51

4

5

6

7

12 20 28

14 22 30

13 2921

15 3123

36

37

38

39

44 52 60

46 54 62

45 6153

47 6355

Im

Re

d





2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)


2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)




0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y


0 10 20 30 40 50 600

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y






16 QAM 64 QAM



(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117


2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119875119899 = [[1 00119879 119875119899]]

(21)


min119899

100381610038161003816100381611988311989901 minus 119904119899119894 10038161003816100381610038162 = min119899

10038161003816100381610038161199041198990119894 + 120585 (119896) minus 119904119899119894 10038161003816100381610038162 (22)





Im

Re

0 4 8 12

13951

2 6 10 14

1573 11


0

1

2

3

8 16 24 32 40 48 56

10 18 26 34 42 50 58

9 25 41 5717 33 49

11 27 43 5919 35 51

4

5

6

7

12 20 28

14 22 30

13 2921

15 3123

36

37

38

39

44 52 60

46 54 62

45 6153

47 6355

Im

Re

d





2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)


2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)




0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y


0 10 20 30 40 50 600

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y






16 QAM 64 QAM



(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117


2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)


2 4 6 8 10 12

OFDM

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3

OFDM-DSI (ND = 1)




0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y


0 10 20 30 40 50 600

200

400

600

800

1000

1200

1400

1600

1800

2000

Constellation index

Freq

uenc

y






16 QAM 64 QAM



(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117


2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











16 QAM 64 QAM



(119881119879 = 03) 126(119881119879 = 03)WHT-DSI (119881119879 = 02) 1103 117


2 4 6 8 10 12

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3




3 4 5 6 7 8 9 10 11 12 13 14

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3






0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Constellation index

Freq

uenc

y


4 6 8 10 12 14 16

CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3





0 10 20 30 40 50 600

500

1000

1500

2000

2500

3000

3500

4000

Freq

uenc

y

Constellation index







35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












35 4 45 5 55 6 65 7 75


CCD

F of

PA

PR

PAPR (dB)

100

10minus1

10minus2

10minus3







52 subcarriers

Pilot tones





3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










3 4 5 6 7 8 9 10 11 12 13 14



Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)


OFDM-OP [NT = 16]





4 6 8 10 12 14

OFDM


Prob

abili

tyX

rarrx

100

10minus1

10minus2

10minus3

PAPR x (dB)






6 Conclusions











Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















Disclosure


Competing Interests


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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